2/3x-5/6=1/4x+1

Solution for 2/3x-5/6=1/4x+1 equation:

2/3x-5/6=1/4x+1

We move all terms to the left:

2/3x-5/6-(1/4x+1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

2/3x-1/4x-1-5/6=0

We calculate fractions


(-240x^2)/432x^2+288x/432x^2+(-108x)/432x^2-1=0

We multiply all the terms by the denominator


(-240x^2)+288x+(-108x)-1*432x^2=0

Wy multiply elements

(-240x^2)-432x^2+288x+(-108x)=0

We get rid of parentheses

-240x^2-432x^2+288x-108x=0

We add all the numbers together, and all the variables

-672x^2+180x=0

a = -672; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-672)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-672}=\frac{-360}{-1344}
=15/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-672}=\frac{0}{-1344}
=0
$